How to secure a fall/spring internship while networking for future internships

Sophomore at semi-target here. I was not able to get an internship over the summer, so I am trying to secure one for this fall (or spring if not fall) to gain some experience to talk about in interviews. Boutique IB or PE seems like the best option and it would probably have to be remote. My question is how do I ask for a fall internship while simultaneously network for a sophomore summer internship as well as begin to build relationships for my junior year internship. It seems like if I begin to cold call boutiques, I will lose my chance to build relationships with them for sophomore summer. However, if I network in the traditional way, I won't be able to get a fall internship in time. Any advice?